摘要
考虑伴随超临界分支的高维非退化系统在非通有假设下的同宿轨道分支问题,通过在未扰同宿轨道邻域建立活动坐标架,导出系统在新坐标系下的全局Poincaré映射,对伴随超临界分支的非通有同宿轨道的保存及分支周期轨道的情况导出相应的分支方程和分支图.
The problem of homoclinic bifurcation accompanied with transcritical bifurcation is studied for the high dimensional system under the nongeneric hypothesis.By constructing local coordinate systems near the unperturbed homoclinic orbit,the Poincaré maps of the system in new coordinate systems are obtained,and the persistence of nongeneric homoclinic orbit and bifurcation of periodic orbit from the homoclinic orbit for the system accompanied with transcritical bifurcation are discussed.The corresponding bifurcation equation and bifurcation graph are given.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2004年第4期401-408,共8页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(10371040)
上海市重点学科建设项目
关键词
超临界分支
同宿分支
局部坐标系
transcritical bifurcation
homoclinic bifurcation
local coordinate systems
